Mathematics

# Write the value of the following integral : $\underset{-\pi / 2}{\overset{\pi/2}{\int}} \sin^5 \, x \, dx$

##### SOLUTION
Let  $f(x)=\sin^{5}x$

$f(-x)=\sin^{5}(-x)$

$f(-x)=-\sin^{5}x=-f(x)$

So $f(x)$ is an odd function.

And for any odd function,
$\int_{-a}^{a}f(x)\: dx=0$

So, the value of the given definite integral is zero.

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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